867 lines
25 KiB
C
867 lines
25 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
static integer c_n1 = -1;
|
|
static real c_b23 = 1.f;
|
|
static real c_b37 = -1.f;
|
|
|
|
/* > \brief \b SLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contrib
|
|
ution to the reciprocal Dif-estimate. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download SLATDF + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slatdf.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slatdf.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slatdf.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, */
|
|
/* JPIV ) */
|
|
|
|
/* INTEGER IJOB, LDZ, N */
|
|
/* REAL RDSCAL, RDSUM */
|
|
/* INTEGER IPIV( * ), JPIV( * ) */
|
|
/* REAL RHS( * ), Z( LDZ, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > SLATDF uses the LU factorization of the n-by-n matrix Z computed by */
|
|
/* > SGETC2 and computes a contribution to the reciprocal Dif-estimate */
|
|
/* > by solving Z * x = b for x, and choosing the r.h.s. b such that */
|
|
/* > the norm of x is as large as possible. On entry RHS = b holds the */
|
|
/* > contribution from earlier solved sub-systems, and on return RHS = x. */
|
|
/* > */
|
|
/* > The factorization of Z returned by SGETC2 has the form Z = P*L*U*Q, */
|
|
/* > where P and Q are permutation matrices. L is lower triangular with */
|
|
/* > unit diagonal elements and U is upper triangular. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] IJOB */
|
|
/* > \verbatim */
|
|
/* > IJOB is INTEGER */
|
|
/* > IJOB = 2: First compute an approximative null-vector e */
|
|
/* > of Z using SGECON, e is normalized and solve for */
|
|
/* > Zx = +-e - f with the sign giving the greater value */
|
|
/* > of 2-norm(x). About 5 times as expensive as Default. */
|
|
/* > IJOB .ne. 2: Local look ahead strategy where all entries of */
|
|
/* > the r.h.s. b is chosen as either +1 or -1 (Default). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrix Z. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] Z */
|
|
/* > \verbatim */
|
|
/* > Z is REAL array, dimension (LDZ, N) */
|
|
/* > On entry, the LU part of the factorization of the n-by-n */
|
|
/* > matrix Z computed by SGETC2: Z = P * L * U * Q */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDZ */
|
|
/* > \verbatim */
|
|
/* > LDZ is INTEGER */
|
|
/* > The leading dimension of the array Z. LDA >= f2cmax(1, N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] RHS */
|
|
/* > \verbatim */
|
|
/* > RHS is REAL array, dimension N. */
|
|
/* > On entry, RHS contains contributions from other subsystems. */
|
|
/* > On exit, RHS contains the solution of the subsystem with */
|
|
/* > entries according to the value of IJOB (see above). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] RDSUM */
|
|
/* > \verbatim */
|
|
/* > RDSUM is REAL */
|
|
/* > On entry, the sum of squares of computed contributions to */
|
|
/* > the Dif-estimate under computation by STGSYL, where the */
|
|
/* > scaling factor RDSCAL (see below) has been factored out. */
|
|
/* > On exit, the corresponding sum of squares updated with the */
|
|
/* > contributions from the current sub-system. */
|
|
/* > If TRANS = 'T' RDSUM is not touched. */
|
|
/* > NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] RDSCAL */
|
|
/* > \verbatim */
|
|
/* > RDSCAL is REAL */
|
|
/* > On entry, scaling factor used to prevent overflow in RDSUM. */
|
|
/* > On exit, RDSCAL is updated w.r.t. the current contributions */
|
|
/* > in RDSUM. */
|
|
/* > If TRANS = 'T', RDSCAL is not touched. */
|
|
/* > NOTE: RDSCAL only makes sense when STGSY2 is called by */
|
|
/* > STGSYL. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IPIV */
|
|
/* > \verbatim */
|
|
/* > IPIV is INTEGER array, dimension (N). */
|
|
/* > The pivot indices; for 1 <= i <= N, row i of the */
|
|
/* > matrix has been interchanged with row IPIV(i). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JPIV */
|
|
/* > \verbatim */
|
|
/* > JPIV is INTEGER array, dimension (N). */
|
|
/* > The pivot indices; for 1 <= j <= N, column j of the */
|
|
/* > matrix has been interchanged with column JPIV(j). */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup realOTHERauxiliary */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > This routine is a further developed implementation of algorithm */
|
|
/* > BSOLVE in [1] using complete pivoting in the LU factorization. */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
|
|
/* > Umea University, S-901 87 Umea, Sweden. */
|
|
|
|
/* > \par References: */
|
|
/* ================ */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > */
|
|
/* > [1] Bo Kagstrom and Lars Westin, */
|
|
/* > Generalized Schur Methods with Condition Estimators for */
|
|
/* > Solving the Generalized Sylvester Equation, IEEE Transactions */
|
|
/* > on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751. */
|
|
/* > */
|
|
/* > [2] Peter Poromaa, */
|
|
/* > On Efficient and Robust Estimators for the Separation */
|
|
/* > between two Regular Matrix Pairs with Applications in */
|
|
/* > Condition Estimation. Report IMINF-95.05, Departement of */
|
|
/* > Computing Science, Umea University, S-901 87 Umea, Sweden, 1995. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void slatdf_(integer *ijob, integer *n, real *z__, integer *
|
|
ldz, real *rhs, real *rdsum, real *rdscal, integer *ipiv, integer *
|
|
jpiv)
|
|
{
|
|
/* System generated locals */
|
|
integer z_dim1, z_offset, i__1, i__2;
|
|
real r__1;
|
|
|
|
/* Local variables */
|
|
integer info;
|
|
real temp;
|
|
extern real sdot_(integer *, real *, integer *, real *, integer *);
|
|
real work[32];
|
|
integer i__, j, k;
|
|
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
|
|
real pmone;
|
|
extern real sasum_(integer *, real *, integer *);
|
|
real sminu;
|
|
integer iwork[8];
|
|
extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
|
|
integer *), saxpy_(integer *, real *, real *, integer *, real *,
|
|
integer *);
|
|
real splus;
|
|
extern /* Subroutine */ void sgesc2_(integer *, real *, integer *, real *,
|
|
integer *, integer *, real *);
|
|
real bm, bp, xm[8], xp[8];
|
|
extern /* Subroutine */ void sgecon_(char *, integer *, real *, integer *,
|
|
real *, real *, real *, integer *, integer *), slassq_(
|
|
integer *, real *, integer *, real *, real *);
|
|
extern int slaswp_(integer *,
|
|
real *, integer *, integer *, integer *, integer *, integer *);
|
|
|
|
|
|
/* -- LAPACK auxiliary routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Parameter adjustments */
|
|
z_dim1 = *ldz;
|
|
z_offset = 1 + z_dim1 * 1;
|
|
z__ -= z_offset;
|
|
--rhs;
|
|
--ipiv;
|
|
--jpiv;
|
|
|
|
/* Function Body */
|
|
if (*ijob != 2) {
|
|
|
|
/* Apply permutations IPIV to RHS */
|
|
|
|
i__1 = *n - 1;
|
|
slaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &ipiv[1], &c__1);
|
|
|
|
/* Solve for L-part choosing RHS either to +1 or -1. */
|
|
|
|
pmone = -1.f;
|
|
|
|
i__1 = *n - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
bp = rhs[j] + 1.f;
|
|
bm = rhs[j] - 1.f;
|
|
splus = 1.f;
|
|
|
|
/* Look-ahead for L-part RHS(1:N-1) = + or -1, SPLUS and */
|
|
/* SMIN computed more efficiently than in BSOLVE [1]. */
|
|
|
|
i__2 = *n - j;
|
|
splus += sdot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &z__[j + 1
|
|
+ j * z_dim1], &c__1);
|
|
i__2 = *n - j;
|
|
sminu = sdot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
|
|
&c__1);
|
|
splus *= rhs[j];
|
|
if (splus > sminu) {
|
|
rhs[j] = bp;
|
|
} else if (sminu > splus) {
|
|
rhs[j] = bm;
|
|
} else {
|
|
|
|
/* In this case the updating sums are equal and we can */
|
|
/* choose RHS(J) +1 or -1. The first time this happens */
|
|
/* we choose -1, thereafter +1. This is a simple way to */
|
|
/* get good estimates of matrices like Byers well-known */
|
|
/* example (see [1]). (Not done in BSOLVE.) */
|
|
|
|
rhs[j] += pmone;
|
|
pmone = 1.f;
|
|
}
|
|
|
|
/* Compute the remaining r.h.s. */
|
|
|
|
temp = -rhs[j];
|
|
i__2 = *n - j;
|
|
saxpy_(&i__2, &temp, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
|
|
&c__1);
|
|
|
|
/* L10: */
|
|
}
|
|
|
|
/* Solve for U-part, look-ahead for RHS(N) = +-1. This is not done */
|
|
/* in BSOLVE and will hopefully give us a better estimate because */
|
|
/* any ill-conditioning of the original matrix is transferred to U */
|
|
/* and not to L. U(N, N) is an approximation to sigma_min(LU). */
|
|
|
|
i__1 = *n - 1;
|
|
scopy_(&i__1, &rhs[1], &c__1, xp, &c__1);
|
|
xp[*n - 1] = rhs[*n] + 1.f;
|
|
rhs[*n] += -1.f;
|
|
splus = 0.f;
|
|
sminu = 0.f;
|
|
for (i__ = *n; i__ >= 1; --i__) {
|
|
temp = 1.f / z__[i__ + i__ * z_dim1];
|
|
xp[i__ - 1] *= temp;
|
|
rhs[i__] *= temp;
|
|
i__1 = *n;
|
|
for (k = i__ + 1; k <= i__1; ++k) {
|
|
xp[i__ - 1] -= xp[k - 1] * (z__[i__ + k * z_dim1] * temp);
|
|
rhs[i__] -= rhs[k] * (z__[i__ + k * z_dim1] * temp);
|
|
/* L20: */
|
|
}
|
|
splus += (r__1 = xp[i__ - 1], abs(r__1));
|
|
sminu += (r__1 = rhs[i__], abs(r__1));
|
|
/* L30: */
|
|
}
|
|
if (splus > sminu) {
|
|
scopy_(n, xp, &c__1, &rhs[1], &c__1);
|
|
}
|
|
|
|
/* Apply the permutations JPIV to the computed solution (RHS) */
|
|
|
|
i__1 = *n - 1;
|
|
slaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);
|
|
|
|
/* Compute the sum of squares */
|
|
|
|
slassq_(n, &rhs[1], &c__1, rdscal, rdsum);
|
|
|
|
} else {
|
|
|
|
/* IJOB = 2, Compute approximate nullvector XM of Z */
|
|
|
|
sgecon_("I", n, &z__[z_offset], ldz, &c_b23, &temp, work, iwork, &
|
|
info);
|
|
scopy_(n, &work[*n], &c__1, xm, &c__1);
|
|
|
|
/* Compute RHS */
|
|
|
|
i__1 = *n - 1;
|
|
slaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
|
|
temp = 1.f / sqrt(sdot_(n, xm, &c__1, xm, &c__1));
|
|
sscal_(n, &temp, xm, &c__1);
|
|
scopy_(n, xm, &c__1, xp, &c__1);
|
|
saxpy_(n, &c_b23, &rhs[1], &c__1, xp, &c__1);
|
|
saxpy_(n, &c_b37, xm, &c__1, &rhs[1], &c__1);
|
|
sgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &temp);
|
|
sgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &temp);
|
|
if (sasum_(n, xp, &c__1) > sasum_(n, &rhs[1], &c__1)) {
|
|
scopy_(n, xp, &c__1, &rhs[1], &c__1);
|
|
}
|
|
|
|
/* Compute the sum of squares */
|
|
|
|
slassq_(n, &rhs[1], &c__1, rdscal, rdsum);
|
|
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of SLATDF */
|
|
|
|
} /* slatdf_ */
|
|
|